{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 7\n",
    "\n",
    "May 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the libraries \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Euler's method\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func( t, y ): \n",
    "    return (t**2 + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Approximate solution at x =  2  is  6.625000\n"
     ]
    }
   ],
   "source": [
    "def func( t, y ): \n",
    "    return (t**2 + 1) \n",
    "      \n",
    "# Function for euler formula \n",
    "def euler( t0, y, h, t ): \n",
    "    temp = -0\n",
    "  \n",
    "    # Iterating till the point at which we \n",
    "    # need approximation \n",
    "    while t0 < t: \n",
    "        temp = y \n",
    "        y = y + h * func(t0, y) \n",
    "        t0 = t0 + h \n",
    "    return(y)\n",
    "\n",
    "# Initial Values \n",
    "t0 = 1\n",
    "y0 = 4\n",
    "h = 0.5\n",
    "  \n",
    "# Value of x at which we need approximation \n",
    "t = 2\n",
    "y = euler(t0, y0, h, t) \n",
    "print(\"Approximate solution at x = \", t, \" is \", \"%.6f\"% y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ts = np.linspace(2, 7, 100)\n",
    "ys = [euler(t0, y0, h, i) for i in ts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analytic_sol(t):\n",
    "    return(t**3/3 + t +8/3)\n",
    "\n",
    "ytruth = [analytic_sol(i) for i in ts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts, ys, label=\"Euler approximate h = %0.2f  \" % h );\n",
    "plt.plot(ts, ytruth, label='Analytic solution')\n",
    "plt.legend();\n",
    "plt.title(\"Euler's Method\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7smseb76Z7cOQxdMrs33WjYj0wPYhbXP7AcHWg6+UoZkvcPOBX6WUckX2od3zUVE81bEj5ZOT+XLDBqRs2RvbZvjMK69kK+hFpDXwJvCoMeZShlX/BeaKyHhsH8ZWAXbkuMoCzs/Pj3379mW67tixY/lbjFLq9nbtwpQvT5+xY/k9OpoNGzbgaeEMpVk5vTIcaAJ4iUgM8C62s2yKAhH2Mze2GWNeMsbsF5H5wAEgGXjZ5PSMG6WUcja7d/MfLy/mz5/PmDFj+Mc//mFpObcNemNMZid7Tr9F+w+AD3JSlFJKOa3Ll9lz4AADRWjVqhWDBw+2uiKdAkEppXLTn9u20Tk1Fc+SJZk1a1amV5rnN+eYAkEppZyAMYbegwdzFFg3ZYrDXDxn/VuNg1uyZAkikuNJtXr27Jl+sc7NXD+db16N661fv54nnnjilm3OnTvH5MmT05+fPHkyfUIwpVTmJk+ezIKoKD7w8KDRU09ZXU46DfrbSLsK9ZtvvsnzY10f9Fu2bMnzY97M9UHv4+Nz2zcqpQqyyMhIXnvtNR4rVYrB9eqBA82FpEF/CxcvXmTz5s1Mnz79mqBfv349TZo0oVOnTlSrVo2wsLD0uWRGjhxJSEgItWrVok+fPjfMMbNmzRrat2+f/jwiIoIOHTpkOp1vxsukP/zwQ/z9/aldu3amV14uWLCAWrVqUbt2bRo3bgzY5uHp1asX/v7+BAUFsW7duhu2yzgdMUCtWrU4duwYQ4YM4bfffiMwMJDBgwdz7NgxatWqdcv9zpgxgw4dOtC6dWuqVKnCG2+8cWf/4Eo5qYSEBDp16sQ999zDrMRECtWpY3VJ13CKMfqBAwdmexbJmwkMDOST20yW9u2339K6dWseeughypYty65du6hj/wHu3r2b/fv34+PjQ8OGDdm8eTOPPPII/fr1S7+cvlu3bixbtownn3wyfZ/NmjXj5ZdfJj4+Hm9vb7766it69erFk08+ec10vhktX76cb7/9lu3bt1OsWDESEhJuaDNy5EhWrlxJxYoVOXfuHACfffYZYJu07JdffqFly5YcOnQoS/8+Y8aMYd++fen1ZDxf/1b73bNnD7t376Zo0aJUrVqV/v37U6lSpRv2r5SrSE1NpXv37pw8eZJNs2bh+fTTEBRkdVnX0B79LYSHh9O1a1cAunbtSnh4ePq6evXq4evrS6FChQgMDEwPwnXr1lG/fn38/f1Zu3Yt+/fvv2afIkK3bt2YPXs2586dY+vWrelzptzM6tWr6dWrF8WKFQOgbCZX1zVs2JCePXvy+eefp9/IY9OmTXTr1g2AatWqcd9992U56G/lVvtt3rw5pUqVwsPDgxo1amR7wjKlnMXYsWP5/vvvmTBhAvXSZll1sKB3ih797XreeeHMmTOsXbuWffv2ISKkpKQgInz44YcA10zVmzaNbmJiIn379iUyMpJKlSoxYsSITCcIS+vBe3h40Llz5/SbYdyMMea2c59PnTqV7du38/333xMYGMiePXsynZr4ehmnXIabT7t8fT03k9m/i1Kuau3atbzzzjt07dqVvn37wqBB4OEB1atbXdo1tEd/EwsXLqR79+78/vvvHDt2jOjoaO6//342bdp0023SQtLLy4uLFy/e9MNLHx8ffHx8GDVqFD179kxfnnE634xatmzJl19+mX77wMyGbn777Tfq16/PyJEj8fLyIjo6+pqpiQ8dOsTx48epWrXqNdv5+fmxa9cuAHbt2sXRo0cBKFGiRPqNUq6Xlf0q5epiYmLo2rUrDz30ENOmTbN1xnbvBn9/uE3nLb9p0N9EeHj4NR+aAnTs2JG5c+fedJvSpUvzwgsv4O/vT2hoaPpdlDITFhZGpUqVqFGjRvqyjNP5ZtS6dWvatm1LcHAwgYGB13x4mmbw4MH4+/tTq1YtGjduTO3atenbty8pKSn4+/vTpUsXZsyYcU2PO+01JSQkEBgYyJQpU3jooYcA8PT0pGHDhtSqVeuGK/uysl+lXFlSUhKdO3fm8uXLLF68mBIlStjmoty92+GGbeDv6YUtFRwcbCIjI69ZdvDgQao72J8/ualfv34EBQWlz4muCi5X/7/uEk6dggULwP75V/9Fi5i0cSMLevakU9p9pS9cgGHDYMoUeOmlfClLRKKMMcG3a+dYf18UEHXr1uXuu+/m448/troUpVRWfPwxjBsHwBxs91Z9Deg0Y8a17dzcwH56syPRoLdA2m0IlVJOYudOqFuXnyZM4IVWrWgcFMSYJUvA3f3adkWLgv3sOEfi0EGflbNNlHJmjjB0qm4jNRWiokjo3Jn2PXpQpkwZ5i9ejLuDzGOTFQ4b9B4eHpw5cwZPT08Ne+WSjDGcOXMGDw8Pq0tRt3L4MCkXLhC2YwcxMTFs2LCB8uXLW13VHXHYoPf19SUmJgZHvXG4UrnBw8MDX19fq8tQtxIZyQhgxb59TJ069Zob3zsLhw16d3d37rfw1ltKKQWwODycUcDzvXrRp08fq8vJFj2PXimlbmL//v10X76c+sWL89mUKU47jKxBr5RSmTh79iyhoaGUSE1lUZcuTn1RoMMO3SillFVSUlJ45pln+P3YMdYBFZs0sbqkHNEevVJKXWfo0KGsWLGCSWFhNAQIvu3Fpw5Ne/RKKZXBnDlzGDduHH379qWPCBQvDvY5oJyV9uiVUsouMjKS3r1707hxY9v06JGRULcuFHLuqHTu6pVSKpfExsYSGhpKuXLlWLhwIe7GwJ49cItZaJ2FDt0opQq8xMRE2rdvz7lz59i8eTPe3t62KYevXHH68XnIQtCLyJfAE0CcMaaWfVlZYB7gBxwDnjLGnBXbSaafAo8Bl4CexphdeVO6Ukpl05EjtiDHNhXFC5MmsX37dhYPGkTtQ4fg0CHYsMHWtiAEPTAD26ycszIsGwKsMcaMEZEh9udvAm2AKvZHfWCK/atSSjmOTp3gp58AGAfMBt4H2l9/Ux8fH3jggfyuLtfdNuiNMRtExO+6xe2AJvbvZwLrsQV9O2CWsU3Jt01ESotIBWNMbG4VrJRSOfLnn/Dzz/DKKyytXJkhAwbQpVUr3h43Dq6/8rVChRuXOaHsjtGXTwtvY0ysiKTN11kRiM7QLsa+7IagF5E+QB+Ae++9N5tlKKXUHYqMBGPY89BDhL35JsHBwXy1eDFy111WV5Zncvusm8ze+jKdcNsYM80YE2yMCfb29s7lMpRS6ia2b+cPoO3o0ZQuXZqlS5dylwuHPGS/R38qbUhGRCoAcfblMUClDO18gZM5KVAppXLT5c2bCfXw4MzZs2zatIkKFSpYXVKey26P/r9AD/v3PYClGZZ3F5sGwHkdn1dKOYrUlBR6rF7NjsREZs+eTVBQkNUl5YusnF4Zju2DVy8RiQHeBcYA80XkeeA40Nne/Adsp1YewXZ6Za88qFkppbJl+MCBLLhyhXHt29O+fXury8k3WTnr5umbrGqeSVsDvJzTopRSKrfNnDmTDyZN4gXg9bfesrqcfKVTICilXN66det44YUXaF6pEp8VLYrUrm11SflKp0BQSrm0gwcP0r59e6pUqcLC4sVxv/decHe3uqx8pT16pZTLOnXqFI899hgeHh788O23lP75Z6hf8C7W1x69UsolXbp0ibZt2xIXF8ePP/7IfefPQ2IiNGhgdWn5Tnv0SimXk3YrwMjISObOnUtwcDBs325bqT16pZRyQufP2+awwTYb5YDhw1m6dCmT3n+fdnXqQHQ0/Pijbe6aSpVuszPXo0GvlHJuZ87AvffCpUsAfAR8BgwGXh42DIYN+7tthw4uMUnZndKgV0o5t02bbCE/fDhzY2N54/PP6RISwpgXXrjxFoAtWlhTo8U06JVSzm3LFnB3Z02DBvRs144mTZowc8UKChUtanVlDkM/jFVKObfNm/mpWjXad+lC1apVWbJkCUU15K+hPXqllPO6coVjO3fSxt2dUmXKsHz5ckqXLm11VQ5Hg14p5bTiV6+mVVISl93d2bRiBb6+vlaX5JA06JVSTunixYs8/q9/cRxYHR5OzZo1rS7JYWnQK6WcTlJSEp06dWJXTAxLKlSg4ZNPWl2SQ9OgV0o5ldTUVHr27MnKlSv5onhxnmzZ0uqSHJ6edaOUchrGGAYMGEB4eDhjBg3i+YsX4R//sLosh6dBr5RyGiNHjmTSpEkMGjSIN2rUsC1s2NDaopyABr1SyilMmjSJESNG0KtXLz788ENkyxYoXRqqV7e6NIenQa+UcnizZs2if//+hIaGMm3aNEQENm+2DdtcP82BuoF+GKuUciwHDsCAAXD1KgDfnj7Nc/v307x0acLPnMHtn/8EY+DgQXj2WYuLdQ76VqiUciyzZsG6dQCsOXuWLgcOEFyiBN/WqoVHWu9dBFq2hKeesrBQ56E9eqWUY9mwAerVY/MHH9C2ZUuq1qrFD+vXU7xsWasrc1rao1dKOY6//oKdO9lVtSqPPfYYvr6+REREUFZDPkc06JVSjmPrVg4kJ9Ny8WLKlCnD6tWrKV++vNVVOT0NeqWUwzi0eDHNgSLFirFmzRoqFcDb/uWFHAW9iLwqIvtFZJ+IhIuIh4jcLyLbReSwiMwTkSK5VaxSynUdPXqU5tOnk+Lmxpq1a3nwwQetLsllZDvoRaQi8AoQbIypBRQGugJjgQnGmCrAWeD53ChUKeW6oqOjada0KZeSklj9zDNU14ugclVOh27cgLtExA0oBsQCzYCF9vUzgdAcHkMp5cJOnDhBs2bNSDh9mpVAQKdOVpfkcrId9MaYE9huuH4cW8CfB6KAc8aYZHuzGKBiZtuLSB8RiRSRyPj4+OyWoZRyYrGxsTRr1oxTp06x8plnCBaBRx6xuiyXk5OhmzJAO+B+wAe4G2iTSVOT2fbGmGnGmGBjTLC3t3d2y1BKOalTp07RrFkzTpw4wfLly2nwv/9BQACUKWN1aS4nJ0M3/wSOGmPijTFXgcXAP4DS9qEcAF/gZA5rVEq5mLi4OJo1a8bx48f54YcfaBgSAlu2wKOPWl2aS8rJlbHHgQYiUgy4DDQHIoF1QCfgG6AHsDSnRSqlnNiFC7Z5aeziEhJo2rcvR0+e5IcJE2js4QHffAOXL2vQ55FsB70xZruILAR2AcnAbmAa8D3wjYiMsi+bnhuFKqWcVM+esHgxAHFAU+Ao8APQpG/fv9u5uUGjRvlfXwGQo7lujDHvAu9et/h/QL2c7Fcp5SKSkyEiAkJD+aNjR5q//TZHT53i+3ffpUnt2te29fEB/bwuT+ikZkqpvLNzJ1y4wMnWrWk2ahTRp0/z/fLlNG3a1OrKChQNeqVU3lmzhhNA0w8/5OSpU6xYsYJGOjyT7zTolVJ55vfvv6dZkSLEx8ezcuVKGur9XS2hk5oppfLEb/v20XjbNs6IEBERoSFvIe3RK6Vy3a+//krzpk1JBNaOG0ed+vWtLqlA0x69UipX/fzzzzRu3Jirly6xrnBh6vTqZXVJBZ726JVSuWbnzp20atWKYsWKsfr++6lWpgwUL251WQWe9uiVUrli48aNNG/enNKlS7Nx2TKqHTgAzZtbXZZCg14plQuWL19Oq1atqFixIhs3buT+o0fBGA16B6FDN0qpO7NoERw6lP503s8/8+z8+fjfcw8rO3TAe9YsWLUKihUD/RDWIWjQK6WyLj4eOne29daBz4EXgYbAspMnKfXvf//dNiwMiuidRB2BDt0opbIuIgKMwWzcyJj336cP0KplS1YmJFAqMREyPr7+2upqlZ326JVSWbdiBallyzJ40SLGf/IJTz/9NDNmzKCI9twdmvbolVJZk5rK1RUreK5UKcZ/8gn9+vVj9uzZGvJOQINeKZUll7Zto318PDOPHuW9995j4sSJFCqkEeIMdOhGKXVbZ86c4YmuXdkBTB07lhffeMPqktQd0LdjpdQt/f777zRq1IjdMTEs8PPTkHdC2qNXSt3UTz/9RJs2bbj011+sLFSIR7t2tboklQ3ao1dKZWrNmjU0atSIwoULs+m993g0JQVat7a6LJUNGvRKqRt8/fXXtGnThvvuu4+tW7dS65dfoEQJePhhq0tT2aBDN0oVZJcuwaefwuXLABhjGLVxI8N//JFmfn4satOG0tNcoN9cAAAWfUlEQVSmwbff2uat0VMpnZIGvVIFWXg4vPUWAFeBl4Avge7A58eOUeSjj2ztCheGZ56xqEiVUzp0o1RB9t13UKkS5xISaNO8OV8Cw4YNY0ZqKkWMgdRU2+PqVdscN8opaY9eqYIqMREiIjjaoQOPN2zIkSNHmDFjBj169LC6MpXLNOiVKqjWrmXbpUu0W7aMJGDVqlU0adLE6qpUHsjR0I2IlBaRhSLyi4gcFJGHRaSsiESIyGH71zK5VaxSKveEjx9PE6B4mTJs3bpVQ96F5XSM/lNghTGmGlAbOAgMAdYYY6oAa+zPlVIOwhjDiHff5Zk1a6jv6cmOnTupVq2a1WWpPJTtoRsRKQk0BnoCGGOSgCQRaQc0sTebCawH3sxJkUqp3HHp0iV69uzJggUL6AVMHT2aIp6eVpel8lhOevQPAPHAVyKyW0S+EJG7gfLGmFgA+9dymW0sIn1EJFJEIuPj43NQhlIqK2JiYmjUqBELFy7kwxYtmA4UadfO6rJUPshJ0LsBdYApxpgg4C/uYJjGGDPNGBNsjAn29vbOQRlKqdvZtm0bISEhHD58mO+++47BZ88iDRpAuUz7YcrF5OSsmxggxhiz3f58IbagPyUiFYwxsSJSAYjLaZFKqSw6fx62bk2/pyvAV6tW8dKkSfh6ebFm3DhqXL4MkZHwwQcWFqryU7aD3hjzh4hEi0hVY8yvQHPggP3RAxhj/7o0VypVSt3ea6/Bl18CtitdBwETgX8C8/74g7IvvWRrJwKhoRYVqfJbTs+j7w/MEZEiwP+AXtiGg+aLyPPAcUAvp1MqP1y9CkuWQGgo8S++SJd33mFdVBSvdu3Kh/364eaW4de9dGmoWtW6WlW+ylHQG2P2AMGZrGqek/0qpbJh3To4e5aoRo1o36cP8fHxzJw5k+7du1tdmbKYXhmrlKtYtIhZRYrw4ttvU65cOTZt2kTdunWtrko5AJ3UTCkXcOXSJfp+/TU9kpJ4+OGHiYyM1JBX6TTolXJyMTExPBoSwpTLl3mjbVtWrVqFnrKsMtKgV8qJRUREEBQUxP7Dh1no7s7YOXOu/dBVKTTolXJKqampvP/++7Rq1Yry5cuzs2xZOj72GBQvbnVpygHpW79STub06dN069aNFStW8OyzzzL1+ee5u2lT6NjR6tKUg9KgV8qRvf46bNqU/nTzhQt0OXKE08nJTPHz48Vff0V69gQ3N3jiCevqVA5Ng14pRxUdDePHg78/qT4+fHT0KG8dPozfXXexNSSEoJIlbe08PeGll6CM3vpBZU6DXilHNW8eAHGff06PESNYcegQnTt35osvvqBkWsgrlQUa9Eo5qvBw1lWtSlj79iQkJDB16lT69OmDiFhdmXIyGvRKOaCr+/YxYtcuRotQtWpVVqxYQUBAgNVlKSelp1cq5WCOHj1K4zZt+DfQq0sXdu7cqSGvckSDXikHMnfuXAIDAzlw8iTf1KjB9PBwiuu58SqHNOiVcgDnz5/n2WefJSwsDP/77+en1FS6DBxodVnKRegYvVIW27BhA927dycmJoaRI0cy9OxZ3A4c0AugVK7RoFcqv0RHQ3AwnDsHwBVjGJ6SwrjUVB4ANrm50WDUKEhKsl38VLastfUql6FBr1R++eoriI+H11/n54QEui9bxk9xcfQJDOTjZs0oXqSIrZ0IdOtmba3KpWjQK5UfUlNhxgxSmjZlnKcnwz/9lLJly/Ldd9/xhE5doPKYBr1S+WHjRg4dPUpPNze2Dh1Kp06dmDJlCl5eXlZXpgoADXql8lhKSgoTBw3iLeCu06eZM2cOTz/9tF7hqvKNBr1Seejw4cM816MHmyIjeeLee/nP1q34+PhYXZYqYPQ8eqXyQEpKCh9//DEBAQHs3bOHmcB/w8M15JUltEevVC7bv38/zz//PNu3b6dt27ZM+eMPfM6fh4cftro0VUBp0CuVXRERMGgQpKQAcCU1lX+fPs3o06cpWagQ4b6+dDl8GDl4EEaPtp02qZQFchz0IlIYiAROGGOeEJH7gW+AssAuoJsxJimnx1HK4bz3HvzxBzRqxJYzZ3ghKooDFy4QVqkSE2rXxrtoUVu74GDo3dvaWlWBlhs9+gHAQSDtTghjgQnGmG9EZCrwPDAlF46jlOPYuxc2b+bc++8z9MQJpi5aRKVKlfhh3jzatGljdXVKXSNHH8aKiC/wOPCF/bkAzYCF9iYzgdCcHEMpR2SmTGG+mxs1Jk1i2rRpvPrqqxw4cEBDXjmknPboPwHeAErYn3sC54wxyfbnMUDFHB5DKYfy288/8/K0aaxMSaFOxYp89/331K1b1+qylLqpbPfoReQJIM4YE5VxcSZNzU227yMikSISGR8fn90ylMo3iYmJvP/++9QKDmZLSgoTX32VHTt2aMgrh5eTHn1DoK2IPAZ4YBuj/wQoLSJu9l69L3Ays42NMdOAaQDBwcGZvhko5ShWrFhB//79OXLkCE+VKsWEihXx+fhjPZNGOYVsB70xZigwFEBEmgCDjDFhIrIA6ITtzJsewNJcqFOpvHf0KOzefc2iY3FxvD5jBou3b+chHx9W9e1Li8mTYexYDXnlNPLiPPo3gW9EZBSwG5ieB8dQKnelpEDLlnDkCACXgXHAaGzjmx8Ar588SdHJk6FMGXjmGetqVeoO5UrQG2PWA+vt3/8PqJcb+1Uq33z3HRw5gpk4kUVJSQwaP57fT57kqZYt+ej116l0zz1/ty1fHkqUuPm+lHIwemWsUgDjx/NThQoMXLSI9T/+SEBAAGtnz6Zp06ZWV6ZUjmnQqwLvj+XLGbZxI9NFKJuUxJQpU+jduzdubvrroVyDzl6pCqzLly8zevRoqrRty0xgYN++HD58mJdeeklDXrkU/d+sCpzU1FRmz57N22+/TUxMDO2Acc89R5VJk6wuTak8oUGvXNeSJXDy2ss4Ig4e5M2lS9kdE0Pwvfcyu1EjHt2yBYYPt6hIpfKeBr1yTZs3Q4cO6U93YzvvNwLwA2YDTx8/TqHjx6FbN7jvPkvKVCo/6Bi9ck2jRoGXF4c3bKBraCh1gKgyZRg/ciS/REcTFhdHobg4iIuDGTOsrlapPKU9euV6du4kZsUKRtWrxxdNm1K0aFHeeustBg8eTOnSpa2uTql8p0GvXEpcXByju3ZlCpC6ezcvvvgiw4YN456MFzwpVcBo0CuXcObMGT766CP+79NPuXz5Mj0CAxm+ZAl+fn5Wl6aU5TTolfNISIDExGsXnT3L+GnT+HT6dP66dIkuFSsy4uxZqq5da5uTRimlQa+cRHg4PPsspKYCcBoYD/wfcBHoDLwL1IyJgaFDNeSVykCDXjm+xER44w0ICOCPZ55h/OrVTP7xRy4lJdG5Th2GPf44tSrab2Tm7g5PPWVtvUo5GA165fg++4zjMTGMCw7mi+HDSUpKokuXLrzzzjvUqFHD6uqUcnga9MqhHdi+nbFvvcVcEVi2jO7duzNkyBCqVKlidWlKOQ29YEo5pC1bthAaGkrNBg1YkJTEy1278ttvvzF9+nQNeaXukPbolTXOnIGIiGsWpaam8t2uXYxbtozNv/5KmbvvZpibG/2feALvuXMtKlQp56dBr/JfcjI0bQp79wJwCZgFTAAOAfcCnwLP/fUXxYsXh3HjLCtVKVegQa/y33/+A3v3cuLDD/nsyBH+M28eCefPE1yrFt/06kXHli3/ng++XDkoW9baepVychr0Kl+Z+Hi2Dx3KxPLlWfDWW6SkpBAaGsrAgQNp1KgRImJ1iUq5HA16lS8SExNZsGAB//f66+y8cIGSxtCvXz/69+/PAw88YHV5Srk0DXqVOy5ftn3Aep1j0dFMnT2b6d98w+mEBKoCnzVtSrelSylRokT+16lUAaRBr3IuLg7q1IETJwBIAZYDU+xfBWgLvAw09/JCFi8GDXml8o0Gvcq5/v0hPp7o997jy8hIpm/eTHRCAhVKleKdRo3o/cgj3OvpaWv76KOgc8Irla806FWOXF24kGXz5zP9oYdY/t57GGNo0aIFE/r0oW3btri7u1tdolIFXraDXkQqYTv9+R4gFZhmjPlURMoC87DdmvMY8JQx5mzOS1WOZP/+/cyYOpVZkycTB/hcvMiQIUPo3bs3999/v9XlKaUyyEmPPhl43RizS0RKAFEiEgH0BNYYY8aIyBBgCLb7MitnkZwM330H585dszjh4kW+2bGDGZs3s/PoUdxEeMIYen/yCa1efvnvc9+VUg4l27+ZxphYINb+/QUROQhUBNoBTezNZgLr0aB3LsOHw+jRACQBPwBfA98BV4EAbFexPmMM5YYPhwEDrKpUKZUFudIFExE/IAjYDpS3vwlgjIkVkXI32aYP0Afg3nvvzY0yVG5Yu5bU0aPZ3KYNc8qUYf7333P2/HnKeXnRr107urVvT2DNmrYLm9zdwcfH6oqVUreR46AXkeLAImCgMebPrF7ZaIyZBkwDCA4ONjmtQ+WMMYY969YR3rYt37i5Eb18OcWKFSM0NJSwsDBaZpyWQCnlVHL0mysi7thCfo4xZrF98SkRqWDvzVcA4nJapMohYyA6Ov02fH8vNuz79Vfmf/8985Yt4/CxY7gBrR55hNEvvUS7du1sk4oppZxaTs66EWA6cNAYMz7Dqv8CPYAx9q9Lc1ShyhljoFs3mDPH9hT4GVgALAR+xXZTgqbAIKDjyJF4DhtmUbFKqbyQkx59Q6AbsFdE9tiXvYUt4OeLyPPAcWz3bVZWGTuW1Dlz2NG5M4svXmRxVBS/xcVRSIQm1arxSnAwHevWpXypUuDtDW3aWF2xUiqX5eSsm03Yrm7PTPPs7lfljitXrrB27FiWvvsu//XwIHbBAtzd3WnevDlvtG9P+/bt8fb2trpMpVQ+0E/XnNGRI+k37cgo7tw5fti1i+8iI1m1Zw8XExMpXqgQrdu0IbRjRx5//HFK6/QDShU4GvTOZvt2aNYMLl0iFdgNfG9/7MQ2Bl8ReBZ4smRJmu3YgUfVqtbVq5SynAa9M/nlF+LbtCGieHFWPPooK7dvJy4hARGhXq1ajHjkEZ5o3JigatVs57nfd59OIKaU0qB3dFeuXGHLli1ELF7MqmnT2JWUhAE8d+ygZatWtGnThlatWlGuXKbXpSmllAa95XbuhLCw9Jt2pBjD7pQU1l69ypqrV9mYnMxlbD+oBoULM7JvX1r26EHdunUpXLiwpaUrpZyDBr2VtmwhpXVr9hYvzroaNVh/4gQbTp7k3JUrANQoW5YXfH1pUakSj/r6UuK556BePYuLVko5Gw36fJaUlERUVBQbZ85kwxdfsMkYzl+4ALGxVK5cmY7PPkuzZs1o1qwZ99xzj9XlKqVcgAZ9bjIGxo6F8eNtU/0CCampbE1JYXNyMluSk9menEyivXnVIkV4qnNnGrduzaOPPkqlSpWsq10p5bI06HNLUhLJL7zA/lmz2FajBtuMYWtsLL+ePw+AW6FCBHp58S8fHx6pUIGGlStT/u23oXx5iwtXSrk6DfrbiY6GPXtuWGyM4bfYWCKPHGHn4cPsXL+eqPPnuQRw4ABeXl483KgR3Rs0oGHDhoSEhFCsWLF8L18ppTTob+Xrr+Ff/yL1r784gu3ipF1AlP2Rdv+lokCQCC+0akW97t2pX78+DzzwAFmdslkppfJSwQt6Y26Yrjejv/76i32Rkfw0bBg/bdnCTyVL8tNdd3Hx8mUAiri7E1ClCk9VrUrd6tUJqVGDWpUr416pkt6EQynlkApO0BsDM2fC4MFw+jRXgcPAfmCf/fEz8Bu2aQQAShQpQm1/f3oGBVGnTh2CgoKoUaMGRYoUseY1KKVUNjh30KekwNWrt2xy6dIlDm3axMG33+bgvn0c9PTkgLc3h86cIdnesy8kQuWyZQm85x66lStHwD33EBAail+nThQqVCg/XolSSuUZ5w76xYvhqadIBo4BR4BD2Hrqv9ofxzM0LyTCA2XKUKNGDdrVrEn16tWpVasW1atXx8PDI9/LV0qp/ODUQf9DQgIDPD05dvZseu8coGTRojzk5UUjb2+qeXtTtXx5qnXvTpVGjTTQlVIFjlMHvXedOgQ1a8ZTVapQuXJlKleuTNWqVfH29tYzXpRSys6pgz4kJIT58+dbXYZSSjk0/aRRKaVcnAa9Ukq5OA16pZRycRr0Sinl4jTolVLKxWnQK6WUi9OgV0opF6dBr5RSLk6MMbdvlddFiMQDv2dzcy/gdC6W4wz0NRcM+poLhpy85vuMMd63a+QQQZ8TIhJpjAm2uo78pK+5YNDXXDDkx2vWoRullHJxGvRKKeXiXCHop1ldgAX0NRcM+poLhjx/zU4/Rq+UUurWXKFHr5RS6hY06JVSysU5bdCLSCURWSciB0Vkv4gMsLqmvCYiHiKyQ0R+sr/m96yuKT+ISGER2S0iy6yuJb+IyDER2Ssie0Qk0up68pqIlBaRhSLyi/13+mGra8pLIlLV/rNNe/wpIgPz7HjOOkYvIhWACsaYXSJSAogCQo0xBywuLc+I7f6IdxtjLoqIO7AJGGCM2WZxaXlKRF4DgoGSxpgnrK4nP4jIMSDYGFMgLh4SkZnARmPMFyJSBChmjDlndV35QUQKAyeA+saY7F44ektO26M3xsQaY3bZv78AHAQqWltV3jI2F+1P3e0P53ynziIR8QUeB76wuhaVN0SkJNAYmA5gjEkqKCFv1xz4La9CHpw46DMSET8gCNhubSV5zz6MsQeIAyKMMa7+mj8B3gBSrS4knxlglYhEiUgfq4vJYw8A8cBX9iG6L0TkbquLykddgfC8PIDTB72IFAcWAQONMX9aXU9eM8akGGMCAV+gnojUsrqmvCIiTwBxxpgoq2uxQENjTB2gDfCyiDS2uqA85AbUAaYYY4KAv4Ah1paUP+zDVG2BBXl5HKcOevs49SJgjjFmsdX15Cf7n7brgdYWl5KXGgJt7ePV3wDNRGS2tSXlD2PMSfvXOGAJUM/aivJUDBCT4a/ThdiCvyBoA+wyxpzKy4M4bdDbP5icDhw0xoy3up78ICLeIlLa/v1dwD+BX6ytKu8YY4YaY3yNMX7Y/rxda4x51uKy8pyI3G0/wQD7EEZLYJ+1VeUdY8wfQLSIVLUvag647EkV13maPB62AdufTM6qIdAN2GsfswZ4yxjzg4U15bUKwEz7p/SFgPnGmAJzymEBUh5YYuvL4AbMNcassLakPNcfmGMfyvgf0MvievKciBQDWgAv5vmxnPX0SqWUUlnjtEM3SimlskaDXimlXJwGvVJKuTgNeqWUcnEa9Eop5eKc+fRKpe6YiHgCa+xP7wFSsF1+D3DJGPMPSwpTKg/p6ZWqwBKREcBFY8xHVteiVF7SoRul7ETkov1rExH5UUTmi8ghERkjImH2ewHsFZEH7e28RWSRiOy0Pxpa+wqUypwGvVKZqw0MAPyxXYH9kDGmHrbpkvvb23wKTDDGhAAd0amUlYPSMXqlMrfTGBMLICK/Aavsy/cCTe3f/xOoYZ+qAKCkiJSw3x9BKYehQa9U5q5k+D41w/NU/v69KQQ8bIy5nJ+FKXWndOhGqexbBfRLeyIigRbWotRNadArlX2vAMEi8rOIHABesrogpTKjp1cqpZSL0x69Ukq5OA16pZRycRr0Sinl4jTolVLKxWnQK6WUi9OgV0opF6dBr5RSLu7/AX4k3Tsqx+oVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for count, h in enumerate([ 1,0.5, 0.2, 0.1, 0.001]):\n",
    "    ys = [euler(t0, y0, h, i) for i in ts]\n",
    "    ytruth = [analytic_sol(i) for i in ts]\n",
    "    plt.xlabel('Time')\n",
    "    plt.plot(ts, ys, label=\"Euler approximate h = %0.3f  \" % h, color='red' );\n",
    "    plt.plot(ts, ytruth, label='Analytic solution', color='black')\n",
    "    plt.legend();\n",
    "    plt.title(\"Euler's Method\");\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(t, y): \n",
    "    return (t**2 + 1) \n",
    "      \n",
    "        \n",
    "class Euler():\n",
    "    def __init__(self, t0=t0, y0=y0, h=h, func=func):\n",
    "        self.t0 = t0\n",
    "        self.y0 = y0\n",
    "        self.h = h\n",
    "        self.func = func\n",
    "  \n",
    "    def euler(self, t): \n",
    "        temp = -0\n",
    "        y = self.y0\n",
    "        t0 = self.t0\n",
    "        while t0 < t: \n",
    "            y = y + self.h * self.func(t0, y) \n",
    "            t0 = t0 + self.h \n",
    "        return(float(y))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func(t, y): \n",
    "    return (3*y) \n",
    "\n",
    "method = Euler(0, 2, 0.1, func)\n",
    "method.euler(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3800000000000003"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "method.euler(0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func(t, y): \n",
    "    return (np.log(t)) \n",
    "\n",
    "method = Euler(1, 0, 1, func)\n",
    "method.euler(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "method.euler(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytic exact solution =  0.3862943611198906\n"
     ]
    }
   ],
   "source": [
    "sol = 2* np.log(2) -2 +1 \n",
    "print('Analytic exact solution = ', sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7000000000000001\n",
      "0.3714397757435194\n"
     ]
    }
   ],
   "source": [
    "h=1\n",
    "soleuler = 0.0\n",
    "while np.abs([soleuler-sol])>0.05:\n",
    "    h-=0.1\n",
    "    method = Euler(1, 0, h, func)\n",
    "    soleuler = method.euler(2)\n",
    "print(h)\n",
    "print(soleuler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sol(t):\n",
    "    return(t*np.log(t)-t+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts=np.linspace(1, 3, 100)\n",
    "for count, h in enumerate([1,0.7,0.4,0.1]):\n",
    "    method = Euler(1, 0, h, func)\n",
    "    ys = [method.euler(i) for i in ts]\n",
    "    ytruth = [sol(i) for i in ts]\n",
    "    plt.xlabel('Time')\n",
    "    plt.plot(ts, ys, label=\"Euler approximate h = %0.2f  \" % h, color='#A60628' );\n",
    "    plt.plot(ts, ytruth, label='Analytic solution', color='black')\n",
    "    plt.axvline(x=2, ymin=0, ymax=1, color='red')\n",
    "    plt.legend();\n",
    "    plt.title(\"Euler's Method\");\n",
    "    \n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func(t, y): \n",
    "    return (-3*y) \n",
    "\n",
    "method = Euler(0, 2, 0.1, func)\n",
    "method.euler(0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sol(t):\n",
    "    return(2*np.exp(-3*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hJjOC+s8//+Thhx8mODiYNWvW6NOYLi4uLo7q1atbXUaOcPToUZ5++mn27t17x7Jbgxj5+vpaUJlyVlr/nkUk2hgTmtG6efJMH2x3IAwfPpx169axevVqq8tRSqkcIc+GPsCLL76Iv78/w4YNc3xQppSr8/f3T/MsH2x/BehZft6Wp0Pf09OTd999lx07drBgwQKry1FKKcvl6dAH6Nq1KyEhIbz99ts6gIZSyuXl+dB3c3Nj0qRJJCQk3HbLm1JKuaI8H/pgu5e3ZcuWjB07lqSkJKvLUUopy7hE6ANMnDiRv/76i7Fjx1pdinJhS5cuRUQeuMOvXr16OR4MSk/qjgcbNmz4QPtMz4YNG3j66afv2ubcuXPMmDHDMX3y5ElHZ2Uqe7lM6NesWZO+ffsyffp0R8+BSmW3W0+/ZseNBalD/6effsryfaYndej7+fll+KalsobLhD7Yul7Onz8/Q4cOtboU5YIuXLjA5s2bmTNnzm2hv2HDBpo0acIzzzxDtWrV6Natm6NvmzFjxhAWFkbNmjXp16/fHX3erF27lnbt2jmmV69eTfv27dPsgrhQoUKOdhMnTiQoKIhatWo5ngxO6euvv6ZmzZrUqlWLiIgIwNYvUO/evQkKCqJ27dqsX7/+jvVSdqEMtpOto0ePMmzYMA4dOkRISAhvvPEGR48epWbNmnfd7ty5c2nfvj0tWrQgICCAN998895+4CpNea7DtbspXbo0w4YNY8SIEWzcuJFHH33U6pKUBQYOHHjfvV2mJyQkhClTpty1zbJly2jRogVVqlTBx8eHmJgY6tSpA8COHTuIjY3Fz8+P8PBwNm/eTKNGjXjllVccj/R3796d7777jlatWjm2+dhjj/Hyyy9z+vRpSpYsyWeffUbv3r1p1arVbV0Qp7Ry5UqWLVvG1q1b8fb2TnOI0TFjxrBq1SrKlCnDuXPnAJg+fTpg61Bt3759NG/enAMHDjj18xk/fjx79+511HP06FHHsrttd+fOnezYsQNPT0+qVq3KgAEDbuuSWN07lzrTBxgyZAjlypVj0KBB6Q62oFRWiIyMpHPnzgB07tyZyMhIx7J69epRtmxZ3NzcCAkJcYTi+vXrqV+/PkFBQaxbt47Y2NjbtikidO/enS+//JJz586xZcsWWrZsedc61qxZQ+/evfH29gbAx8fnjjbh4eH06tWL2bNnO/6fbNq0ie7duwNQrVo1KlSo4HTo383dttusWTOKFi2Kl5cXgYGB992ZmvoflzrTB1uf5hMnTqRLly7MmzePPn36WF2SymYZnZFnhaSkJNatW8fevXsREW7cuIGIMHHiRIDbuhe+1fXvlStXeOmll4iKiqJcuXKMHj06zWdNbp3Ze3l50bFjR8fAHukxxmTYF9XMmTPZunUrK1asICQkhJ07d6bZnXJqKbuJhvS7ik5dT3rS+rmoB+NyZ/oAnTp1omHDhrz99tuOgSiUykqLFy+mR48eJCQkcPToUY4fP07FihXZtGlTuuvcCkxfX18uXLiQ7geffn5++Pn5MXbsWHr16uWYn7IL4pSaN2/Op59+6hgiMa3LO4cOHaJ+/fqMGTMGX19fjh8/flt3ygcOHODYsWNUrVr1tvX8/f2JiYkBICYmhiNHjgBQuHDhdP+vObNdlXlcMvRFhClTpvDbb7/x3nvvWV2OcgGRkZG3feAK0KFDB+bPn5/uOsWKFeOFF14gKCiItm3bOkaHSku3bt0oV64cgYGBjnkpuyBOqUWLFrRu3ZrQ0FBCQkJu++D1ljfeeIOgoCBq1qxJREQEtWrV4qWXXuLGjRsEBQXRqVMn5s6de9uZ+K1jOnv2LCEhIXz00UeOQYxKlChBeHg4NWvW5I033rhtHWe2qzJPnu1a2Rm9evUiMjKSvXv3EhAQkC37VNbI610rv/LKK9SuXdvRp7vK27Rr5fs0fvx4PD09bxsHVKncpm7duuzevZvnnnvO6lJULuDSoV+qVClGjRrFihUrWLFihdXlKHVfoqOj+fHHH/WSiHKKS4c+wIABA6hatSoDBw7k6tWrVpejslBOu5Sp1P140H/HLh/6+fPnZ+rUqcTHx6c7HqjK/by8vEhKStLgV7maMYakpCS8vLzuexsu/UFuSu3ateM///kPcXFxlC9fPtv3r7LW9evXSUxM1DEVVK7n5eVF2bJlyZcv323znf0gV0PfLiEhgerVq9OiRQuWLFmS7ftXSqkHoXfv3KMKFSowYsQIli5dysqVK60uRymlsoSe6adw7do1goODuX79Onv37qVAgQKW1KGUUvdKz/TvQ/78+Zk+fTqHDx9mwoQJVpejlFKZTkM/lWbNmtGlSxfGjRuXKT0IKqVUTqKhn4YPPviAAgUK8OKLL+otfkqpPEVDPw2lSpViwoQJrF+/ni+++MLqcpRSKtM4Ffoi0kJE9otIvIjcMbaaiHiKyEL78q0i4m+fn09E5onIHhGJE5G3Mrf8rPPCCy/wyCOPMHjwYM6cOWN1OUoplSkyDH0RcQemAy2BQKCLiASmatYX+MMYUxmYDNz6FLQj4GmMCQLqAv1vvSHkdG5ubsyaNYvz58/f0RWsUkrlVs6c6dcD4o0xh40x14AFQJtUbdoA8+zfLwaaiW1oHgMUFBEPoABwDfgzUyrPBkFBQbzxxhvMnTuXtWvXWl2OUko9MGdCvwxwPMV0on1emm2MMcnAeaAEtjeAi8Ap4BgwyRhzxzA9ItJPRKJEJOr06dP3fBBZacSIEQQEBNCvXz8uXrxodTlKKfVAnAn9tAbTTH1LS3pt6gE3AD+gIjBERCrd0dCYj40xocaY0JIlSzpRUvYpUKAAn3zyCYcPH2bkyJFWl6OUUg/EmdBPBMqlmC4LnEyvjf1STlHgLNAV+MEYc90Y8zuwGcjwibGcJiIigv79+zNlyhS2b99udTlKKXXfnAn97UCAiFQUkfxAZ2B5qjbLgZ72758B1hnbDe7HgMfEpiDQANiXOaVnrwkTJlCqVCn69u3LtWvXrC5HKaXuS4ahb79G/wqwCogDFhljYkVkjIi0tjebA5QQkXhgMHDrts7pQCFgL7Y3j8+MMbsz+RiyRdGiRZk1axZ79uzRwdSVUrmWdrh2j3r06EFkZCTbtm2jdu3aVpejlFKAdriWZaZMmYKvry+9e/fWyzxKqVxHQ/8e+fj4MGvWLHbt2sW4ceOsLkcppe6Jhv59aN26NV27dmXs2LHExMRYXY5SSjlNQ/8+/fvf/6ZkyZL06NFDx11VSuUaGvr3ycfHhzlz5hAbG6sPbSmlcg0N/QfQsmVL+vXrx6RJk9i0aZPV5SilVIY09B/Q+++/T8WKFenZsyd//fWX1eUopdRdaeg/oEKFCjFv3jyOHj3KwIEDrS5HKaXuSkM/EzRq1Ihhw4bx6aefsmTJEqvLUUqpdGnoZ5LRo0cTGhrKCy+8wIkTJ6wuRyml0qShn0ny5cvHl19+yZUrV+jVqxc3b960uiSllLqDhn4mqlq1Kh988AFr1qxh8uTJVpejlFJ30NDPZP369aNdu3a89dZb5OSO45RSrklDP5OJCJ988gl/+9vf6NKli97GqZTKUTT0s4CPjw/z58/n8OHDvPzyy1aXo5RSDhr6WaRx48aMHDmSL774gnnz5lldjlJKARr6WWr48OE0adKEl156iV9++cXqcpRSSkM/K7m7uzN//nwKFSpEx44duXjxotUlKaVcnIZ+FitdujRffvklcXFxDBgwwOpylFIuTkM/GzzxxBMMHz6czz77jLlz51pdjlLKhWnoZ5NRo0bx2GOP8Y9//INdu3ZZXY5SykVp6GcTd3d3IiMj8fHxoUOHDpw7d87qkpRSLkhDPxs99NBDfP311yQkJNCzZ0/tn0cple009LNZw4YNmTRpEsuXL2f8+PFWl6OUcjEa+hZ49dVX6dKlC8OHD+eHH36wuhyllAvR0LfArf55goOD6dKlC4cOHbK6JKWUi9DQt4i3tzdLlixBRGjXrp0+uKWUyhYa+haqVKkSCxYsIDY2VgdeUUplCw19izVv3pyJEyeyePFixo4da3U5Sqk8zsPqAhQMHjyY3bt3M2rUKGrWrEn79u2tLkkplUfpmX4OICLMmjWL+vXr0717d31iVymVZZwKfRFpISL7RSReRIalsdxTRBbal28VEf8Uy4JFZIuIxIrIHhHxyrzy8w4vLy+WLl1K8eLFadWqFadOnbK6JKVUHpRh6IuIOzAdaAkEAl1EJDBVs77AH8aYysBkYIJ9XQ/gS+BFY0wNoAlwPdOqz2NKly7Nt99+S1JSEm3atOHy5ctWl6SUymOcOdOvB8QbYw4bY64BC4A2qdq0AW4ND7UYaCYiAjQHdhtjdgEYY5KMMTcyp/S8qXbt2syfP5+oqCjtqkEplemcCf0ywPEU04n2eWm2McYkA+eBEkAVwIjIKhGJEZE309qBiPQTkSgRiTp9+vS9HkOe06ZNGyZOnMjXX3/NiBEjrC5HKZWHOHP3jqQxzzjZxgNoBIQBl4C1IhJtjFl7W0NjPgY+BggNDU29bZc0ZMgQDh48yD//+U/8/f154YUXrC5JKZUHOHOmnwiUSzFdFjiZXhv7dfyiwFn7/I3GmDPGmEvA90CdBy3aFYgI06dPp0WLFvzjH/9g5cqVVpeklMoDnAn97UCAiFQUkfxAZ2B5qjbLgZ72758B1hljDLAKCBYRb/ubwaOAjhDuJA8PDxYtWkRQUBDPPvssO3bssLokpVQul2Ho26/Rv4ItwOOARcaYWBEZIyKt7c3mACVEJB4YDAyzr/sH8AG2N46dQIwxZkXmH0beVbhwYVasWEHx4sX5+9//zpEjR6wuSSmVi4nthDznCA0NNVFRUVaXkeP88ssvNGrUCF9fX3766Sd8fX2tLkkplYPYPy8NzaidPpGbSwQGBvLtt99y/Phxnn76ae2VUyl1XzT0c5Hw8HAWLFjA9u3b6dixI9euXbO6JKVULqOhn8u0adOGWbNmsXLlSu2OWSl1z7SXzVzo+eefJykpiWHDhlG8eHGmTZuG7QFopZS6Ow39XGro0KEkJSXxr3/9Cx8fH959912rS1JK5QIa+rnYhAkT+OOPPxg7diyFChVi6NChVpeklMrhNPRzMRFh5syZXLhwgWHDhlGwYEFeeeUVq8tSSuVgGvq5nLu7O59//jmXL19mwIABeHt706dPH6vLUkrlUHr3Th6QL18+Fi5cSPPmzXn++ef58ssvrS5JKZVDaejnEZ6enixdupSmTZvSs2dPIiMjrS5JKZUDaejnId7e3ixfvpzGjRvz3HPPsWjRIqtLUkrlMBr6eUzBggX57rvvCA8Pp2vXrixcuNDqkpRSOYiGfh5UqFAhVqxYQcOGDenatSvz58+3uiSlVA6hoZ9HFS5cmJUrVxIREUH37t35/PPPrS5JKZUDaOjnYQULFmTFihU0bdqUXr16MXv2bKtLUkpZTEM/j/P29ubbb7+lRYsW9OvXjylTplhdklLKQhr6LqBAgQIsXbqU9u3bM2jQIN577z2rS1JKWURD30V4enqycOFCnnvuOYYPH86bb75JThs1TSmV9bQbBhfi4eHBvHnzKFq0KP/6179ISkpi1qxZeHjoPwOlXIX+b3cxbm5u/Pvf/3Z0x3zu3Dm++uorvLy8rC5NKZUN9PKOCxIRxowZw5QpU1iyZAktW7bk/PnzVpellMoGGvou7LXXXuOrr75i8+bNREREcPLkSatLUkplMQ19F9e1a1dWrFjB4cOHadiwIXFxcVaXpJTKQhr6iieeeIKNGzdy5coVGjZsyI8//mh1SUqpLKKhrwCoU6cOP//8M6VKleKJJ57QrpmVyqM09JWDv78/P/30E4888ghdu3Zl7Nixei+/UnmMhr66TfHixVm1ahXPPfccI0aMoEePHly9etXqspRSmUTv01d38PT05PPPP6dq1aqMGDGCI0eOsHTpUkqWLGl1aUqpB6Rn+ipNIsLw4cNZuHAh0dHRhIWFsXv3bqvLUko9IA19dVfPPvssP/74I9evX6dhw4YsXbrU6pKUUg/AqdAXkRYisl9E4kVkWBrLPUVkoX35VhHxT7W8vIhcEJHXM6dslZ3CwsKIioqiRo0atG/fntGjR3OVHka/AAAVkklEQVTz5k2ry1JK3YcMQ19E3IHpQEsgEOgiIoGpmvUF/jDGVAYmAxNSLZ8MrHzwcpVVSpcuzcaNG+nRowfvvPMObdu21a4blMqFnDnTrwfEG2MOG2OuAQuANqnatAHm2b9fDDQTEQEQkbbAYSA2c0pWVvHy8mLu3LlMnTqVlStXUq9ePX2CV6lcxpnQLwMcTzGdaJ+XZhtjTDJwHighIgWBocA7D16qyglEhAEDBrB27VrOnTtHWFgYCxcutLospZSTnAl9SWNe6id20mvzDjDZGHPhrjsQ6SciUSISdfr0aSdKUlaLiIggJiaGWrVq0blzZwYOHMi1a9esLksplQFnQj8RKJdiuiyQujtGRxsR8QCKAmeB+sBEETkKDATeFpFXUu/AGPOxMSbUGBOq94LnHmXKlGHDhg0MHDiQDz/8kEcffZSEhASry1JK3YUzob8dCBCRiiKSH+gMLE/VZjnQ0/79M8A6Y9PYGONvjPEHpgD/NMZMy6TaVQ6QL18+Jk+ezKJFi4iNjaV27dp8++23VpellEpHhqFvv0b/CrAKiAMWGWNiRWSMiLS2N5uD7Rp+PDAYuOO2TpW3dezYkZiYGPz9/WndujVDhgzRyz1K5UCS0zrUCg0NNVFRUVaXoe7TlStXeP3115k+fTp169YlMjKSgIAAq8tSKs8TkWhjTGhG7fSJXJWpvLy8mDZtGsuWLePIkSPUrl2befPmaW+dSuUQGvoqS7Rp04Zdu3YRGhpKr1696NSpE2fPnrW6LKVcnoa+yjJly5Zl7dq1jBs3jqVLlxIcHMzatWutLkspl6ahr7KUu7s7w4YN4+eff6ZQoUI8/vjjvPbaa1y6dMnq0pRySRr6KlvUrVuXmJgYBgwYwNSpU6lTpw5bt261uiylXI6Gvso23t7eTJ06lTVr1nDp0iUaNmzIsGHDuHLlitWlKeUyNPRVtmvWrBl79uyhd+/eTJgwwTEou1Iq62noK0sULVqUTz75hB9++IG//vqL8PBwBg8ezMWLF60uTak8TUNfWerJJ59k79699OvXj8mTJ1OzZk1Wr15tdVlK5Vka+spyRYsW5aOPPmLjxo3kz5+f5s2b0717d7THVaUyn4a+yjEiIiLYtWsXI0aMYOHChVSrVo05c+bo0IxKZSINfZWjeHl5MWbMGHbu3ElgYCDPP/88jRs3ZteuXVaXplSeoKGvcqTAwEA2btzIZ599xoEDB6hbty4DBw7UcXmVekAa+irHcnNzo1evXuzfv58XXniBqVOnUqVKFT777DO95KPUfdLQVzmej48PH330Edu2baNSpUr06dOHhg0b6hO9St0HDX2Va4SGhrJ582bmzZtHQkICDRo0oHv37iQmJlpdmlK5hoa+ylXc3Nzo0aMHBw4c4O233+brr7+matWqjBo1igsXLlhdnlI5noa+ypUKFy7Me++9x759+2jVqhVjxowhICCA2bNnk5ycbHV5SuVYGvoqV/P392fBggVs2bKFhx9+mH79+hEcHMyyZct0tC6l0qChr/KEBg0a8N///pdvvvmGmzdv0q5dO8LDw9m4caPVpSmVo2joqzxDRGjfvj179+5l9uzZJCQk0KRJE5o3b8727dutLk+pHEFDX+U5Hh4ePP/888THxzNp0iRiYmKoV68ebdu2ZefOnVaXp5SlNPRVnlWgQAGGDBnC4cOHeeedd9iwYQO1a9emQ4cO7N692+rylLKEhr7K84oUKcLIkSM5evQoI0eOZPXq1dSqVYt27doRExNjdXlKZSsNfeUyihUrxjvvvMPRo0cZNWoU69evp27dujz11FP89NNPVpenVLbQ0Fcux8fHh9GjR5OQkMC7777L1q1bCQ8Pp0mTJqxatUpv9VR5moa+cllFixZl+PDhJCQkMHnyZOLj42nRogW1a9dm/vz5XL9+3eoSlcp0GvrK5RUsWJCBAwdy6NAhPv30U65du0a3bt2oXLky77//Pn/++afVJSqVaTT0lbLz9PSkd+/e7N27l+XLl+Pv78/rr79O2bJlGTJkCEeOHLG6RKUemIa+Uqm4ubnRqlUrNm7cyPbt23nqqaf48MMPqVy5Mu3bt2fjxo163V/lWhr6St1FaGgokZGRHDlyhDfffJONGzfSpEkTatWqxccff8zFixetLlGpe+JU6ItICxHZLyLxIjIsjeWeIrLQvnyriPjb5z8hItEissf+9bHMLV+p7FGuXDnGjRvH8ePH+eSTT3Bzc6N///6UKVOG1157jbi4OKtLVMopGYa+iLgD04GWQCDQRUQCUzXrC/xhjKkMTAYm2OefAVoZY4KAnsAXmVW4Ulbw9vamb9++7Nixg02bNvH3v/+dmTNnEhgYSJMmTYiMjOTKlStWl6lUupw5068HxBtjDhtjrgELgDap2rQB5tm/Xww0ExExxuwwxpy0z48FvETEMzMKV8pKIkJ4eDjz58/n+PHjjB8/nmPHjtG1a1fKlCnD4MGDiY2NtbpMpe7gTOiXAY6nmE60z0uzjTEmGTgPlEjVpgOwwxhzNfUORKSfiESJSNTp06edrV2pHOGhhx5i6NChxMfHs3r1apo1a8a0adOoWbMmDRo04OOPP+b8+fNWl6kU4FzoSxrzUt+6cNc2IlID2yWf/mntwBjzsTEm1BgTWrJkSSdKUirncXNz4/HHH2fRokWcOHGCDz74gAsXLtC/f39KlSpFt27dWL16NTdu3LC6VOXCnAn9RKBciumywMn02oiIB1AUOGufLgssBXoYYw49aMFK5QYlS5Zk0KBB7Nmzh61bt9KnTx++//57mjdvTvny5XnjjTe0p09lCWdCfzsQICIVRSQ/0BlYnqrNcmwf1AI8A6wzxhgRKQasAN4yxmzOrKKVyi1EhHr16jF9+nROnTrFokWLqFu3LlOmTKFWrVoEBQUxbtw4jh49anWpykWIMw+ZiMjfgSmAO/CpMeY9ERkDRBljlouIF7Y7c2pjO8PvbIw5LCLDgbeAgyk219wY83t6+woNDTVRUVH3f0RK5QJnzpxh4cKFREZGsnmz7XzokUceoVOnTnTs2BE/Pz+LK1S5jYhEG2NCM2yX054s1NBXrubo0aNERkaycOFCdu3ahYjQqFEjOnbsSIcOHfQNQDlFQ1+pXGjfvn0sXLiQr7/+mtjYWESEhg0b0qFDB9q1a4e/v7/VJaocSkNfqVwuLi6OxYsX880337Br1y4A6tSpQ5s2bWjbti1BQUGIpHXjnHJFGvpK5SGHDh1iyZIlLFu2jC1btmCMwd/fn1atWtG6dWsiIiLInz+/1WUqC2noK5VH/fbbbyxfvpxvv/2W1atXc+XKFQoXLkzz5s156qmnaNmyJaVKlbK6TJXNNPSVcgGXLl1izZo1fPfdd6xYsYKTJ22P0NSpU4cWLVrQokULGjRoQL58+SyuVGU1DX2lXIwxhl27dvH999+zcuVKtmzZwo0bNyhSpAiPPfYYTz75JE888QSVKlXSzwLyIA19pVzcuXPnWLt2LatWrWLVqlUcO3YMAH9/fx5//HGaNWvGY489xkMPPWRxpSozaOgrpRyMMRw4cIA1a9awevVq1q9f7xj7NygoiKZNm9K0aVMiIiLw8fGxuFp1PzT0lVLpSk5OJiYmhrVr17Ju3To2b97M5cuXERGCgoJ49NFHiYiIoHHjxvztb3+zulzlBA19pZTTrl27xvbt21m/fj0bN27kp59+4tKlSwAEBATQuHFjwsPDCQ8Pp0qVKvqZQA6koa+Uum/Xr18nOjqa//73v2zatIlNmzZx9uxZAHx9fXnkkUccr7CwMAoWLGhxxUpDXymVaW7evMn+/fvZvHkzmzdvZsuWLezfvx8Ad3d3atasSf369alfvz716tWjevXquLu7W1y1a9HQV0plqaSkJLZu3crPP//Mzz//zLZt2xwjhBUsWJC6desSGhpKWFgYoaGhVKpUCTc3Z3pzV/dDQ18pla1u3rzJwYMH2bZtG9u2bSMqKoodO3Zw9apthNSiRYtSu3Zt6tSpQ+3atalduzZVq1bFw8PD4srzBg19pZTlrl+/zt69e4mOjiYmJobo6Gh27drleCMoUKAANWvWJCQkhFq1ajkGlilatKjFlec+GvpKqRwpOTmZffv2sWPHDnbs2MGuXbvYuXOn44NigAoVKhAUFOR41ahRg6pVq+Lp6Wlh5Tmbhr5SKtcwxpCYmMiePXvYvXs3u3fvZs+ePezbt4/k5GTA9oFxQEAANWrUIDAwkMDAQKpXr07VqlXx8vKy+Aisp6GvlMr1rl27xv79+4mNjWXv3r3Exsbyyy+/EB8fz82bNwHbOMQVK1akevXqVKtWjapVqzpeDz30kMs8U+Bs6OsnKEqpHCt//vyOSzwpXblyhQMHDhAXF+d47d+/n7Vr13LlyhVHuyJFilClShUCAgIcXytXrkzlypXx8fFxmTeElPRMXymVZ9y8eZNjx46xf/9+Dhw44Ph68OBBEhISSJl3xYoV4+GHH3a8KlWq5HiVLVs2191VpJd3lFIqhStXrnDkyBHi4+M5ePAg8fHxHDp0iEOHDpGQkOD47ADAw8ODcuXKUalSJfz9/R2vChUqUKFCBfz8/HLcm4Je3lFKqRS8vLyoXr061atXv2NZcnIyiYmJHD58mMOHD3PkyBHH1xUrVvDrr7/e1t7d3Z0yZcpQoUIFypcvT7ly5ShXrhzly5enbNmylCtXLsdePtIzfaWUysDly5dJSEi47XXs2DGOHTtGQkICJ06cuO0vBbA9g1C2bFnKlCnj+FqmTBn8/PwcX0uVKpVpYxvrmb5SSmWSAgUKUK1aNapVq5bm8hs3bvDbb79x/PhxEhMTOX78OMePH+fEiROcOHGCTZs2cfLkSa5du3bHur6+vpQuXZrSpUvz5JNPMnjw4Cw9Fg19pZR6QO7u7vj5+eHn50f9+vXTbGOM4cyZM5w4cYKTJ09y8uRJTpw4walTpxyv1JeRsoKGvlJKZQMRoWTJkpQsWZKQkBDL6tAu75RSyoVo6CullAvR0FdKKReioa+UUi5EQ18ppVyIU6EvIi1EZL+IxIvIsDSWe4rIQvvyrSLin2LZW/b5+0XkycwrXSml1L3K8JZNEXEHpgNPAInAdhFZboz5JUWzvsAfxpjKItIZmAB0EpFAoDNQA/AD1ohIFWPMjcw+kOt/XeTcnv2ZvdkcK1+RQniXK03+ooWtLkUplYs4c59+PSDeGHMYQEQWAG2AlKHfBhht/34xME1snU60ARYYY64CR0Qk3r69LZlT/v/8uf8wa5p2y+zN5nj5ihQif/EiQM7r4yOvEXd3xN0NcXODHNinSp7mIj9uvycjqD3hzSzdhzOhXwY4nmI6EUj9yJmjjTEmWUTOAyXs839OtW6Z1DsQkX5AP4Dy5cs7W/ttCgf402TFJ/e1bq5j4Pr5P7l47BSXjp/i2p9/WV1R3mcM5sZNzI0bmJs5q7+qPC+H9Q+WlQr4PZTl+3Am9NN6j039W0ivjTPrYoz5GPgYbB2uOVHTHfIXLUzpx8PvZ1WllHIZznyQmwiUSzFdFjiZXhsR8QCKAmedXFcppVQ2cSb0twMBIlJRRPJj+2B2eao2y4Ge9u+fAdYZW5/Ny4HO9rt7KgIBwLbMKV0ppdS9yvDyjv0a/SvAKsAd+NQYEysiY4AoY8xyYA7whf2D2rPY3hiwt1uE7UPfZODlrLhzRymllHN0EBWllMoDnB1ERZ/IVUopF6Khr5RSLkRDXymlXIiGvlJKuZAc90GuiJwGEh5gE77AmUwqJzdwteMFPWZXocd8byoYY0pm1CjHhf6DEpEoZz7Bzitc7XhBj9lV6DFnDb28o5RSLkRDXymlXEheDP2PrS4gm7na8YIes6vQY84Cee6avlJKqfTlxTN9pZRS6dDQV0opF5IrQ19EPhWR30VkbzrLRUSm2gdk3y0idbK7xszmxDF3sx/rbhH5SURqZXeNmSmj403RLkxEbojIM9lVW1Zx5phFpImI7BSRWBHZmJ31ZQUn/l0XFZFvRWSX/Zh7Z3eNmU1EyonIehGJsx/Ta2m0ybIMy5WhD8wFWtxleUtsffcHYBuG8aNsqCmrzeXux3wEeNQYEwy8S+7/EGwudz9eRMQdmICt2++8YC53OWYRKQbMAFobY2oAHbOprqw0l7v/nl8GfjHG1AKaAO/bx/XIzZKBIcaY6kAD4GURCUzVJssyLFeGvjHmR2z99qenDfC5sfkZKCYipbOnuqyR0TEbY34yxvxhn/wZ2yhluZYTv2OAAcA3wO9ZX1HWc+KYuwJLjDHH7O1z/XE7ccwGKCwiAhSyt03OjtqyijHmlDEmxv79X0Acd44dnmUZlitD3wlpDeZ+x4DseVhfYKXVRWQlESkDtANmWl1LNqoCFBeRDSISLSI9rC4oG0wDqmMbZnUP8Jox5qa1JWUeEfEHagNbUy3KsgxzZmD03MipAdnzIhFpii30G1ldSxabAgw1xtywnQS6BA+gLtAMKABsEZGfjTEHrC0rSz0J7AQeAx4GVovIf40xf1pb1oMTkULY/lIdmMbxZFmG5dXQd8kB2UUkGPgEaGmMSbK6niwWCiywB74v8HcRSTbGLLO2rCyVCJwxxlwELorIj0AtIC+Hfm9gvH3M7XgROQJUI5ePtS0i+bAF/lfGmCVpNMmyDMurl3eWAz3sn4A3AM4bY05ZXVRWEpHywBKgex4/8wPAGFPRGONvjPEHFgMv5fHAB/g/oLGIeIiIN1Af2/XgvOwYtr9sEJG/AVWBw5ZW9IDsn0/MAeKMMR+k0yzLMixXnumLSCS2T/J9RSQRGAXkAzDGzAS+B/4OxAOXsJ0t5GpOHPNIoAQww372m5ybeyh04njznIyO2RgTJyI/ALuBm8Anxpi73tKa0znxe34XmCsie7Bd8hhqjMnt3S2HA92BPSKy0z7vbaA8ZH2GaTcMSinlQvLq5R2llFJp0NBXSikXoqGvlFIuRENfKaVciIa+Ukq5kFx5y6ZSmUFESgBr7ZOlgBvAafv0JWNMQ0sKUyoL6S2bSgEiMhq4YIyZZHUtSmUlvbyjVBpE5IL9axMR2Sgii0TkgIiMt49dsE1E9ojIw/Z2JUXkGxHZbn+FW3sESqVNQ1+pjNUCXgOCsD1JWcUYUw9bP0cD7G0+BCYbY8KADvZlSuU4ek1fqYxtv9XviYgcAv5jn78HaGr//nEgMEWPn0VEpLC9v3SlcgwNfaUydjXF9zdTTN/kf/+H3IBHjDGXs7Mwpe6VXt5RKnP8B3jl1oSIhFhYi1Lp0tBXKnO8CoTaB7H+BXjR6oKUSovesqmUUi5Ez/SVUsqFaOgrpZQL0dBXSikXoqGvlFIuRENfKaVciIa+Ukq5EA19pZRyIf8fOgObLIDMBZUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts=np.linspace(1, 2, 100)\n",
    "for count, h in enumerate([1,0.7, 0.3, 0.03]):\n",
    "    method = Euler(0,2, h, func)\n",
    "    ys = [method.euler(i) for i in ts]\n",
    "    ytruth = [sol(i) for i in ts]\n",
    "    plt.xlabel('Time')\n",
    "    plt.plot(ts, ys, label=\"Euler approximate h = %0.2f  \" % h, color='#A60628' );\n",
    "    plt.plot(ts, ytruth, label='Analytic solution', color='black')\n",
    "    plt.legend();\n",
    "    plt.title(\"Euler's Method\");\n",
    "    \n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
